The drift diffusion model (DDM) is a model of sequential sampling with diffusion (Brownian) signals, where the decision maker accumulates evidence until the process hits a stopping boundary, and then stops and chooses the alternative that corresponds to that boundary. This model has been widely used in psychology, neuroeconomics, and neuroscience to explain the observed patterns of choice and response times in a range of binary choice decision problems. This paper provides a statistical test for DDM's with general boundaries. We first prove a characterization theorem: we find a condition on choice probabilities that is satisfied if and only if the choice probabilities are generated by some DDM. Moreover, we show that the drift and the boundary are uniquely identified. We then use our condition to nonparametrically estimate the drift and the boundary and construct a test statistic.
We provide an axiomatic analysis of dynamic random utility, characterizing the stochastic choice behavior of agents who solve dynamic decision problems by maximizing some stochastic process (Ut) of utilities. We show first that even when (Ut) is arbitrary, dynamic random utility imposes new testable across-period restrictions on behavior, over and above period-by-period analogs of the static random utility axioms. An important feature of dynamic random utility is that behavior may appear history-dependent, because period-t choices reveal information about Ut, which may be serially correlated; however, our key new axioms highlight that the model entails specific limits on the form of history dependence that can arise. Second, we show that imposing natural Bayesian rationality axioms restricts the form of randomness that (Ut) can display. By contrast, a specification of utility shocks that is widely used in empirical work violates these restrictions, leading to behavior that may display a negative option value and can produce biased parameter estimates. Finally, dynamic stochastic choice data allows us to characterize important special cases of random utility—in particular, learning and taste persistence—that on static domains are indistinguishable from the general model.
We model the joint distribution of choice probabilities and decision times in binary decisions as the solution to a problem of optimal sequential sampling, where the agent is uncertain of the utility of each action and pays a constant cost per unit time for gathering information. We show that choices are more likely to be correct when the agent chooses to decide quickly provided that the agent’s prior beliefs are correct. This better matches the observed correlation between decision time and choice probability than does the classical drift-diffusion model, where the agent knows the utility difference between the choices.
We introduce a notion of coarse competitive equilibrium (CCE), to study agents' inability to tailor their consumption to the state of the economy. Our notion is motivated by limited cognitive ability (in particular attention, memory, and complexity) and it maintains the complete market structure of competitive equilibrium. Compared to standard competitive equilibrium, our concept yields riskier allocations and more extreme prices. We provide a tractable model that is suitable for general equilibrium analysis as well as asset pricing.
As demonstrated by the email game of Rubinstein (1989), the predictions of the standard equilibrium models of game theory are sensitive to assumptions about the fine details of the higher order beliefs. This paper shows that models of bounded depth of reasoning based on level-k thinking or cognitive hierarchy make predictions that are independent of the tail assumptions on the higher order beliefs. In addition to this finding, the tools developed in this paper oer a new direction for the analysis of models of bounded depth of reasoning and their applications to various economic settings. (JEL C72, D03)
Models of ambiguity aversion have recently found many applications in dynamic settings. This paper shows that there is a strong interdependence between ambiguity aversion and the preferences for the timing of the resolution of uncertainty, as dened by the classic work of Kreps and Porteus (1978): the modeling choices that are being made in the domain of ambiguity aversion influence the set of modeling choices available in the domain of timing attitudes. The main result of the paper is that the only model of ambiguity aversion that exhibits indierence to timing is the maxmin expected utility of Gilboa and Schmeidler (1989). This paper also examines the structure of the timing nonindierence implied by the other commonly used models of ambiguity aversion. The interdependence of ambiguity and timing that this paper identies is of interest both conceptually and practically–especially for economists using these models in applications.
This paper axiomatizes the robust control criterion of multiplier preferences introduced by Hansen and Sargent (2001). The axiomatization relates multiplier preferences to other classes of preferences studied in decision theory, in particular, the variational preferences recently introduced by Maccheroni, Marinacci, and Rustichini (2006a). This paper also establishes a link between the parameters of the multiplier criterion and the observable behavior of the agent. This link enables measurement of the parameters on the basis of observable choice data and provides a useful tool for applications.
This paper shows that in the class of variational preferences the notion of probabilistic sophistication is equivalent to expected utility as long as there exists at least one event such that the independence axiom holds for bets on that event. This extends a result of Marinacci (2002) and provides a novel interpretation of his result.
An important implication of the expected utility model under risk aversion is that if agents have the same probability belief, then the efficient allocations under uncertainty are comonotone with the aggregate endowment, and if their beliefs are concordant, then the efficient allocations are measurable with respect to the aggregate endowment. We study these two properties of efficient allocations for models of preferences that exhibit ambiguity aversion using the concept of conditional belief, which we introduce in this paper. We provide characterizations of such conditional beliefs for the standard models of preferences used in applications. ∗
We study a deﬁnition of subjective beliefs applicable to preferences that allow for the perception of ambiguity, and provide a characterization of such beliefs in terms of market behavior. Using this deﬁnition, we derive necessary and sufﬁcient conditions for the efﬁciency of ex ante trade and show that these conditions follow from the fundamental welfare theorems. When aggregate uncertainty is absent, our results show that full insurance is efﬁcient if and only if agents share some common subjective beliefs. Our results hold for a general class of convex preferences, which contains many functional forms used in applications involving ambiguity and ambiguity aversion. We show how our results can be articulated in the language of these functional forms, conﬁrming results existing in the literature, generating new results, and providing a useful tool for applications.
In Senegal we encountered a situation in which a minority group of migrant fishermen had completely different sets of expectations regarding a collective action depending on the location where they operated. In one village expectations were pessimistic, while in the other village they were optimistic. Understanding this contrast and its implications provides the main justification for the paper. To be able to account for the contrast between the two areas, pessimistic expectations in the first area have to be traced back to a preceding conflict that could never be settled satisfactorily. A perverse path -dependent process had thus been set in motion that could not be changed by a simple act of will of a determined leadership. To demonstrate the links between expectations and actions that fit with the story told, we propose a simple model of collective action with asymmetric information.